This review examines recent results on analytical modeling of electrostatic MEMS. Such modeling can include multiple coupled physics domains, including electrostatic forces, and lumped circuit models, structural elasticity, rigid body dynamics, or fluid mechanics. This review focuses on analytical models that provide the benefits of a closed-form expression trade rather than strive for the highest degree of accuracy for. Such models have been used successfully for parametric design, synthesis of dynamical models, and development of control laws. This review considers the role of mathematical modeling in several traditional and emerging areas for electrostatic MEMS: 1) analysis of pull-in, 2) effects of parasitics, 3) parametric resonance, 4) movable gate transistor or NEMFETs, and 5) repulsive actuation.

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